Problem: A popular brand of Brazilian coffee costs $\$20$ per pound, and a particular brand of Colombian coffee costs $\$16$ per pound. If you mix $15$ pounds of Brazilian coffee with $5$ pounds of Colombian coffee, how many dollars does one pound of the mixture cost?
The total cost of creating such a mixture is $(15\times\$20)+(5\times\$16)=\$300+\$80=\$380$. The total weight is $15+5=20$ pounds, so each pound will cost $\frac{\$380}{20}=\boxed{\$19}$.